Object models provide abstract information about software structure, but their maintenance is difficult after refactoring takes place. In Model-Driven Development (MDD), effective transferral of model refactoring changes to programs is problematic, especially if these programs are subject to developer manipulation. Consequently, code-driven approaches end up being adopted. We formalize a theory of synchronizers, which are sequences of behavior-preserving program transformations. This theory makes use of invariant-based refactoring, the key idea behind synchronizers. We also establish and prove a soundness theorem for synchronizers. By uncovering the formal requirements for correct refactoring synchronization, the proved properties point out issues - regarding consistency, refactoring automation and quality - that recur in several MDD settings that employ object models.